A Mechanical Theory of Spinning Detonation

Abstract

A review of published experimental data and theoretical discussions of spinning detonation reveals that there does not exist a consistent explanation of all the characteristics of such a phenomenon, particularly the dependence of spinning frequency upon tube diameter. In view of this, it is proposed to treat the problem principally from a hydrodynamic viewpoint by considering a possible periodic fluid motion with a characteristic frequency. It is found that the calculated natural frequencies of vibration of the gaseous products behind a detonation wave agree closely with the measured frequencies of spinning detonation previously published in the literature. An analysis of such vibrations in the light of experimental evidence indicates that the vibratory motion is principally transverse. Of the various possible modes of vibration, the one which is observed depends upon the mixture composition and the tube size. The observed existence of pressure waves in the wake of a spinning detonation wave is probably due to nonuniform combustion at the detonation front. It is shown how the initiation or cessation of combustion in a plane wave gives rise to compression or expansion waves respectively, and how a nonplanar disturbance excites a transverse vibration of characteristic frequency. It is proposed that the uneven combustion of the spinning detonation wave is sustained by the heating and cooling effects of the vibratory pressure waves, which are themselves generated by such irregular combustion; i.e., spinning detonation is a self-excited vibratory phenomenon. Its appearance may thus be-attributed to the susceptibility of the reaction rate to the heating or cooling effects of pressure waves.